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Let $\mathfrak{g}$ be a complex semisimple Lie algebra, $\mathfrak{b}$ be aBorel subalgebra of $\mathfrak{g}$, $\mathfrak{n}$ be the nilradical of$\mathfrak{b}$, and $U(\mathfrak{n})$ be the universal enveloping algebra of$\mathfrak{n}$. We study primitive ideals of $U(\mathfrak{n})$. Almost allprimitive ideals are centrally generated, i.e., are generated by theirintersections with the center $Z(\mathfrak{n})$ of $U(\mathfrak{n})$. Wepresent an explicit characterization of the centrally generated primitiveideals of $U(\mathfrak{n})$ in terms of the Dixmier map and the Kostant cascadein the case when $\mathfrak{g}$ is a simple algebra of exceptional type. (Forclassical simple Lie algebras, a similar characterization was obtained by IvanPenkov and the first author.) As a corollary, we establish a classification ofcentrally generated primitive ideals of $U(\mathfrak{n})$ for an arbitrarysemisimple algebra $\mathfrak{g}$.

Centrally generated primitive ideals of $U(\mathfrak{n})$ for exceptional types